| Full text | |
| Author(s): |
Total Authors: 3
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| Affiliation: | [1] Univ Milano Bicocca, I-20125 Milan - Italy
[2] Univ Sao Paulo, BR-05508 Sao Paulo - Brazil
[3] Politecn Milan, Milan - Italy
Total Affiliations: 3
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| Document type: | Journal article |
| Source: | ADVANCES IN APPLIED PROBABILITY; v. 46, n. 1, p. 256-278, MAR 2014. |
| Web of Science Citations: | 3 |
| Abstract | |
We study an interacting random walk system on Z where at time 0 there is an active particle at 0 and one inactive particle on each site n >= 1. Particles become active when hit by another active particle. Once activated, the particle starting at n performs an asymmetric, translation invariant, nearest neighbor random walk with left-jump probability l(n). We give conditions for global survival, local survival, and infinite activation both in the case where all particles are immortal and in the case where particles have geometrically distributed lifespan (with parameter depending on the starting location of the particle). More precisely, once activated, the particle at n survives at each step with probability P-n is an element of {[}0, 1]. In particular, in the immortal case, we prove a 0-1 law for the probability of local survival when all particles drift to the right. Besides that, we give sufficient conditions for local survival or local extinction when all particles drift to the left. In the mortal case, we provide sufficient conditions for global survival, local survival, and local extinction (which apply to the immortal case with mixed drifts as well). Analysis of explicit examples is provided: we describe completely the phase diagram in the cases 1/2 - l(n) similar to, +/- 1/n(alpha,) P-n= 1 and 1/2 - l(n) similar to +/- 1/n(alpha), 1 - p(n) similar to 1/n(beta)(where alpha, beta > 0). (AU) | |
| FAPESP's process: | 09/52379-8 - Stochastic modeling of interacting systems |
| Grantee: | Fabio Prates Machado |
| Support Opportunities: | Research Projects - Thematic Grants |